onsider the function f given by the rule y = f(x) = x(k − x) k . where k is...

onsider the function f given by the rule y = f(x) = x(k − x) k . where k is some fixed positive constant. (a) Find f(0), f(k) and f(k/2). (b) Sketch the graph of y = f(x) for 0 x k, indicating the turning point. (c) Find the equations of the tangent lines to the curve y = f(x) where the curve crosses the x-axis. (d) Show that the two tangent lines that you found in the previous part in- tersect at a point whose y-value is double the y-value of the turning point you found in part (b